给定 XYZ 网格点，计算内部球体的体积

Question

我有一个由均匀分布的xyz笛卡尔点组成的大型3D网格(~800,000 pts(，我想根据占据球体的点数找到球体内部的体积。我目前正在使用 scipy cKDTree 并检测原点 (0,0,0( 一定半径内的所有点，并用query_ball_point来估计体积，但这个体积(下面的 grid_vol(通常与真实体积 (sphere_vol( 有很大不同(50% 误差或更大(。

import numpy as np
from scipy import spatial
import math
#constants
xl = -3.15
xr =  1.75
yl = -2.0
yr =  2.0
zl = -1.15
zr = 3.9
spacing = 0.05
R = 3.5
cube = spacing ** 3  
#Create grid
x=np.arange(xl,xr,spacing)
y=np.arange(yl,yr,spacing)
z=np.arange(zl,zr,spacing)
x2,y2,z2=np.meshgrid(x,y,z,indexing='ij')
all_grid=np.array([x2.flatten(),y2.flatten(),z2.flatten()]).T
cube = spacing ** 3                  
point_tree = spatial.cKDTree(all_grid)                  # allgrid = evenly spaced rectangular grid
n_voxel = len(point_tree.query_ball_point((0,0,0), R))   # number of points in grid occupying sphere of radius R
grid_vol = n_voxel * cube                               # volume based on grid points
sphere_vol = 4 / 3 * math.pi * R ** 3                # vol of sphere w/ radius R to compare

在这种情况下：

grid_vol = 78.1275
sphere_vol = 179.5944

我想知道是否有一个已知的模块适用于从网格点测量球体的应用

Answer 1

嘿，桂莲，我尝试了你的代码，据我所知，它工作得很好(由于近似值引起的一些错误，但不是很大的错误

import numpy as np
from scipy import spatial
#define constants
l=-1
r=1
spacing=0.05
R=0.5
cube = spacing ** 3  
#Create grid
x=np.arange(l,r,spacing)
y=np.arange(l,r,spacing)
z=np.arange(l,r,spacing)
x2,y2,z2=np.meshgrid(x,y,z,indexing='ij')
all_grid=np.array([x2.flatten(),y2.flatten(),z2.flatten()]).T
# your code            
point_tree = spatial.cKDTree(all_grid)
n_voxel = len(point_tree.query_ball_point((0,0,0), R))   # number of points in grid occupying sphere of radius R
grid_vol = n_voxel * cube                               # volume based on grid points
sphere_volume = 4 / 3 * np.pi * R ** 3
print(grid_vol) # 0.5185000000000001
print(sphere_volume) # 0.5235987755982988